A laser processing machine with redundant actuators includes multiple actuators for moving a position of a laser beam along one direction. Thus, the laser beam is over-actuated, and degrees of freedom are available to optimize the actuation of the laser beam along a desired processing pattern. For example, the laser beam can be positioned by independent operations of the redundant actuators, and thus the task of positioning the laser beam along the processing pattern can be separated between redundant actuators. A reference trajectory for each redundant actuator should be generated such that the combined motion of the actuators results in the laser beam tracking the processing pattern.
Some conventional methods, see, e.g., U.S. Pat. Nos. 5,452,275, 5,798,927, 5,751,585, 6,706,999, use frequency separation techniques to assign the task of positioning the laser beam to two actuators. For example, the processing pattern is filtered by a low pass filter. The filtered signal becomes a reference trajectory for one actuator, while a difference between the processing pattern and the filtered signal becomes a reference trajectory for another actuator. However, the filtering does consider various constraints of the actuators, such as constraints on the accelerations or velocities. Furthermore, there is no guarantee that the separation in frequencies provides the optimal reference trajectories.
One method described in U.S. Publication 2013/0190898 generates the reference trajectories that account for the constraints based on Model Predictive Control (MPC). MPC is based on an iterative, finite horizon optimization of a model of a machine and has the ability to anticipate future events to take appropriate control actions. This is achieved by optimizing the operation of the machine over a future finite time-horizon subject to constraints, and only implementing the control over the current timeslot. For example, the constraints can represent physical limitation of the machine, legitimate and safety limitations on the operation of the machine, and performance limitations on a trajectory. A control strategy for the machine is admissible when the motion generated by the machine for such a control strategy satisfies all the constraints.
For example, at a current time t, a state of the machine is sampled and an admissible cost minimizing control strategy is determined for a relatively short time horizon in the future. Specifically, an online or on-the-fly calculation determines a cost-minimizing control strategy until a future time t+T. Only the first step of the control strategy is implemented, then the state is sampled again and the calculations are repeated starting from the new current state, yielding a new control and new predicted state path. The prediction horizon is continuously shifted forward. For this reason, MPC is also called receding horizon control.
However, due to the tracking nature of the MPC in this problem, such a receding horizon control approach has no guarantee, in general, of finding a solution to the optimization problem. Due to the receding horizon nature of the finite horizon optimal control problem, the existence of the solution for a certain window of data (horizon) does not by itself guarantees that when the data window are shifted, a solution still exists.
Accordingly, there is a need for a method for controlling an operation of a laser processing machine with redundant actuators that guarantees a priori satisfaction of constraints of the operation for variety of processing patterns.